Vector Resonant Research Articles

Static-Errorless Deadbeat Predictive Current Control for PMSM Current Harmonics Suppression Based on Vector Resonant Controller

The traditional deadbeat predictive current control (DPCC) is sensitive to the unmodeled disturbances in permanent magnet synchronous motor (PMSM) drives, including alternating current (AC) and direct current (DC) disturbances, which can lead to intolerable current deviations, especially the current harmonics caused by the AC disturbance. To address the problem, a static-errorless DPCC is proposed for the current loop of PMSM drives. In the studied scheme, a vector resonant controller is used in parallel with the control law of the DPCC to compensate for the AC disturbance, while an extended state observer is used to compensate for the DC disturbance. Thus, the studied scheme is robust to both the AC and DC disturbances. The stability of the proposed scheme is systematically analyzed by the Jury criterion, while the parameter tuning is discussed in detail based on the stability analysis. Compared with the traditional DPCC, the studied scheme can effectively eliminate the current deviations to achieve static-errorless current control in PMSM drives. Finally, the effectiveness of the proposed scheme is validated on a 2.2-kW PMSM platform.

Torque Ripple Suppression of PMSM Using Fractional-Order Vector Resonant and Robust Internal Model Control

Periodic torque ripples caused by current harmonics seriously affect the control accuracy of the Permanent magnet synchronous motors (PMSMs). A conventional approach to reducing current harmonics is the use of a proportional-integral resonant controller in the current loop. Nonetheless, harmonics can still cause steady-state errors. Furthermore, the PI-based control structure is sensitive to parameter mismatches and uncertain disturbances, which will decrease the tracking performance of the current loop. To overcome the drawbacks of the traditional control method, a hybrid robust resonant control strategy was developed in this study. First, a vector resonant controller was enhanced by introducing fractional-order calculus (denoted as the fractional-order vector resonant (FOVR) controller in this article) so that it can suppress harmonic components more effectively. Then, a robust internal mode controller (Robust-IMC) was designed to improve the robustness and dynamic response and further reduce the current harmonics. Finally, by combining the FOVR controller and Robust-IMC, a control method-FOVR-Robust-IMC was designed as the robust control law to ensure satisfactory robustness and harmonics suppression performance. Meanwhile, the stability and robust stability of the developed control strategy were also analyzed. The results demonstrated that the proposed FOVR-Robust-IMC effectively reduced the harmonic components and improved the robustness to parameter mismatch.

Combined Vector Resonant and Active Disturbance Rejection Control for PMSLM Current Harmonic Suppression

A control method that combines a vector resonant controller and an active disturbance rejection control controller is proposed in this article for suppressing the current harmonics of permanent magnet synchronous linear motors. First, the resonant controller is improved by changing its transfer function so that it can suppress current harmonics better. Then, an active disturbance rejection control (ADRC) is designed to suppress the parameter disturbance of motors, which will adversely affect the improved resonant controller. The parameter disturbance is estimated by an extended state observer, and linear feedback control is used for disturbance compensation. The ADRC and the improved resonant controller work together to not only suppress harmonics but also improve resistance against system disturbance. Finally, a linear motor control platform is built, and experimental results are presented to verify the significance and correctness of the proposed approach.

Vector Resonant Relaxation of Stars around a Massive Black Hole

Abstract In the vicinity of a massive black hole, stars move on precessing Keplerian orbits. The mutual stochastic gravitational torques between the stellar orbits drive a rapid reorientation of their orbital planes, through a process called vector resonant relaxation. We derive, from first principles, the correlation of the potential fluctuations in such a system, and the statistical properties of random walks undergone by the stellar orbital orientations. We compare this new analytical approach with numerical simulations. We also provide a simple scheme to generate the random walk of a test star’s orbital orientation using a stochastic equation of motion. We finally present quantitative estimations of this process for a nuclear stellar cluster such as that of the Milky Way.

Evaluation of the three body branching fraction of [formula omitted] by applying the [formula omitted] decay channel

Three body Bc+→J/ψD0K+ decay, which has been recently observed by LHCb collaboration, and are calculated in the model which takes into account the intermediate resonances and nonresonant contributions. In this process, the Bc meson decays first into J/ψ and the quark pair cs¯, and then the quark pair hadronizes into DK components, which undergo final state interaction. The nonresonant contributions arise from the two-body matrix elements of the weak current 〈D0K+|Jμweak|0〉 transition. The Ds+(⁎) mesons are used for intermediate pseudoscalar and vector resonant contributions. The annihilation amplitude arising from the 3-body matrix element of 〈J/ψD0K+|cs¯|0〉 is also associated. Their effects are described in terms of the Breit-Wigner formalism. Because of the Bc+→J/ψD0K+ branching fraction is calculated relative to the Bc+→J/ψπ+ decay, this decay mode is estimated separately, the ratio between the B(Bc+→J/ψD0K+) and B(Bc+→J/ψπ+) to be 0.382±0.084 that is compatible with the experimental data 0.432±0.136±0.028.

Improved control strategy of TFAPF in active distribution networks

In order to solve the deterioration of power quality caused by power electronic devices in active distribution networks, it is necessary to improve the three-phase four-wire active power filters (TFAPF) control strategy. This study adopts the non-harmonic detection and proposes an improved control strategy of TFAPF based on the multi-model principle. Firstly, the mathematical model of TFAPF in the stationary coordinate system is established by replacing the network side current and the DC bus voltage directly as the state variables. Secondly, TFAPF in active distribution networks requires the power fluctuation and fast dynamic response, the proposed control strategy of TFAPF in the stationary coordinate system is applied, namely proportional integral, vector resonant and repetitive control composite controller as the current loop controller of TFAPF with a fast dynamic response, high accuracy and small amount of calculation, provide guarantee for the power quality in active distribution networks. Finally, the feasibility of the proposed control strategy is verified by simulation.

Shunt Active Power Filter Based on Proportional Integral and Multi Vector Resonant Controllers for Compensating Nonlinear Loads

The current tracking control strategy determines the compensation performance of shunt active power filter (SAPF). Due to inadequate compensation of the main harmonic by traditional proportional integral (PI) control, a control algorithm based on PI and multi vector resonant (VR) controllers is proposed to control SAPF. The mathematical model of SAPF is built, and basic principle of VR controller is introduced. Under the synchronous reference frame, the proposed control method based on pole zero cancellation is designed, which narrows the order of the control system and improves the system dynamic response and the control accuracy. Then the feasibility of the method is demonstrated by analyzing the closed loop frequency characteristics of the system. Finally, the simulation and experimental results are carried out to verify the performance of the proposed method.

Analysis About Overshoot Peaks Appearing in the Current Loop With Resonant Controller

Resonant controller is considered ideal for harmonics current control, with advantages of zero steady-state error and computation efficiency. The commonly employed proportional-resonant (PR) controller is widely accepted, but its limited ability in dealing with higher order harmonics, or named limited regulation bandwidth, is also recognized from practical applications. This paper points out that regulation bandwidth of resonant controller is related to the overshoot peaks around resonant frequency in the current loop. The overshoot peaks are caused by open-loop phase lag around resonant frequency, which comes from delay link and $R$ – $L$ plant. The phase lag from delay link could be canceled by the proposed delay-compensated forms for both PR and vector resonant (VR) controller; but toward phase lag from $R$ – $L$ plant, the two types resonant controller perform different: PR controller does not give full consideration about $R$ – $L$ plant, leading to inherent obvious overshoot peaks in current loop, whereas VR controller provides proper leading phase to cancel the phase lag from $R$ – $L$ plant, greatly reducing the overshoot peaks and promising wider regulation bandwidth. The comparisons and analysis reveal the principle and relations of PR and VR controllers, which help to deepen the understanding for further improving the resonant controller.

A Source-Current-Detected Shunt Active Power Filter Control Scheme Based on Vector Resonant Controller

A shunt active power filter (APF) with current detection at the source side is considered as a closed-loop system from the view of the whole power distribution system, which is expected with better harmonics filtering performance compared with the one with load current detection. The conventional source current detection control scheme can be mainly grouped into two types: 1) current-source-based (CS) scheme and 2) power-balance-based (PB) scheme. As introduced in this paper, the CS scheme has good dc-voltage regulation, but it bears inevitable conflict between filtering performance and system stability, whereas the PB scheme has excellent stable filtering performance, but it bears great influence on the dc voltage in the transient state. In this paper, a novel source current detection control scheme is proposed, which reserves the advantages of conventional schemes and, meanwhile, avoids their limitations. The proposed scheme employs a vector resonant controller, with which the shunt APF performs as an equivalent multiband rejection filter that series between nonlinear loads and the grid source, blocking selected harmonics components from the load side flowing into the source side. The proposed scheme is simple in structure, is needless of a harmonics extraction algorithm, and shows good stable and transient performance. Finally, the conclusions obtained in this paper are validated through experiments on the laboratory prototype.

Comparison Analysis of Resonant Controllers for Current Regulation of Selective Active Power Filter with Mixed Current Reference

Instead of extracting every selected harmonic component, the current reference of selective active power filter (APF) can be also obtained by filtering out the fundamental component from distorted load current for computation efficiency. This type of mixed current reference contains kinds of harmonic components and easily involves noises. In this condition, selective harmonic compensation must be realized by the current controller. With regard that selectivity is the most significant feature of controller, this paper presents specific comparison analysis between two types of resonant controllers: proportional-resonant (PR) controller and vector-resonant (VR) controller. The comparison analysis covers the relations, performances, and stability of both controllers. Analysis results conclude that the poorer selectivity of the PR controller could be relatively improved, but limitations from system stability make the improvement hardly realized. By contrast, the VR controller exhibits excellent selectivity and is more suitable for selective APF with mixed current reference. Experimental results from laboratory prototype validate the reasonability of analysis. And the features of each resonant controller are concluded.

The problem of center for resonant singular points of polynomial vector fields

We generalize the notion of “center” to the case of a p : −q resonant singular point of a polynomial vector field in ℂ2 and to some other situations (resonant node, saddle-node, non-elementary singular point of vector field and resonant fixed point of one-dimensional complex diffeomorphism). We show some similarities and differences with the classical case. In particular, the analogue of Bautin's theorem does not hold. Four small amplitude limit cycles can bifurcate from the center after quadratic perturbation of a quadratic vector field with resonant center.